Mathematical problem solving by analogy.

We report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed to reduce or eliminate the difficulty of some of the major processes hypothesized to be involved in analogical transfer. Our studies yielded 4 major findings. First, the process of mapping the features of the source and target problems and the process of adapting the source solution procedure for use in solving the target problem were clearly distinguished: (a) Successful mapping was found to be insufficient for successful transfer and (b) adaptation was found to be a major source of transfer difficulty. Second, we obtained direct evidence that schema induction is a natural consequence of analogical transfer. The schema was found to co-exist with the problems from which it was induced, and both the schema and the individual problems facilitated later transfer. Third, for our multiple-solution problems, the relation between analogical transfer and solution accuracy was mediated by the degree of time pressure exerted for the test problems. Finally, mathematical expertise was a significant predictor of analogical transfer, but general analogical reasoning ability was not. The implications of the results for models of analogical transfer and for instruction were considered.     

Putting lexical constraints in context into the visual-world paradigm

Prior eye-tracking studies of spoken sentence comprehension have found that the presence of two potential referents, e.g., two frogs, can guide listeners toward a Modifier interpretation of Put the frog on the napkin… despite strong lexical biases associated with Put that support a Goal interpretation of the temporary ambiguity (Tanenhaus, M. K., Spivey-Knowlton, M. J., Eberhard, K. M. & Sedivy, J. C. (1995). Integration of visual and linguistic information in spoken language comprehension. Science, 268, 1632–1634; Trueswell, J. C., Sekerina, I., Hill, N. M. & Logrip, M. L. (1999). The kindergarten-path effect: Studying on-line sentence processing in young children. Cognition, 73, 89–134). This pattern is not expected under constraint-based parsing theories: cue conflict between the lexical evidence (which supports the Goal analysis) and the visuo-contextual evidence (which supports the Modifier analysis) should result in uncertainty about the intended analysis and partial consideration of the Goal analysis. We reexamined these put studies (Experiment 1) by introducing a response time-constraint and a spatial contrast between competing referents (a frog on a napkin vs. a frog in a bowl). If listeners immediately interpret on the… as the start of a restrictive modifier, then their eye movements should rapidly converge on the intended referent (the frog on something). However, listeners showed this pattern only when the phrase was unambiguously a Modifier (Put the frog that’s on the…). Syntactically ambiguous trials resulted in transient consideration of the Competitor animal (the frog in something). A reading study was also run on the same individuals (Experiment 2) and performance was compared between the two experiments. Those individuals who relied heavily on lexical biases to resolve a complement ambiguity in reading (The man heard/realized the story had been…) showed increased sensitivity to both lexical and contextual constraints in the put-task; i.e., increased consideration of the Goal analysis in 1-Referent Scenes, but also adeptness at using spatial constraints of prepositions (in vs. on) to restrict referential alternatives in 2-Referent Scenes. These findings cross-validate visual world and reading methods and support multiple-constraint theories of sentence processing in which individuals differ in their sensitivity to lexical contingencies.     

To Matrix, Network, or Hierarchy: That Is the Question

The authors present a structural analysis of three spatial diagrams-matrices, networks, and hierarchies-that specifies 10 properties on which these diagrammatic representations are hypothesized to differ: global structure, building block, number of sets, item/link constraints, item distinguishability, link type, absence of a relation, linking relations, path, and traversal. Each property has a "value" for each diagram, and these property values constitute the applicability conditions for the representations. Twenty-three college students (computer science majors and math educators) selected the type of diagram they thought would be most efficient for organizing the information in each of 18 short scenarios and verbally justified the reasons for their selections. The verbal protocols were coded with respect to the structural analysis. Both the representation selection and verbal justification data provided strong support for the structural analysis. Additionally, a factor analysis of students' justifications indicated that the organization of their knowledge is consistent with the structural analysis. Students' use of the structural properties to select appropriate representations and to justify those selections indicates that the structural analysis has psychological force.     

Training working memory: Limits of transfer

In two experiments (totaling 253 adult participants), we examined the extent to which intensive working memory training led to improvements on untrained measures of cognitive ability. Although participants showed improvement on the trained task and on tasks that either shared task characteristics or stimuli, we found no evidence that training led to general improvements in working memory. Using Bayes Factor analysis, we show that the data generally support the hypothesis that working memory training was ineffective at improving general cognitive ability. This conclusion held even after controlling for a number of individual differences, including need for cognition, beliefs in the malleability of intelligence, and age.     

Understanding Co-Occurring ADHD and Anxiety Symptoms within a Developmental Framework: Risk and Protective Factors of Early Temperament and Peer Relations

Research on Child and Adolescent Psychopathology - Symptoms of ADHD and anxiety often co-occur, yet we are limited in our understanding of which children with ADHD symptoms are more likely to...